Microeconomics--Consumer Theory, how would I solve this problem

"Monet is a first year graduate student and he receives a weekly salary from his teaching assistant job on campus. His stress–release activity is to make strawberry smoothies. Therefore he spends all his weekly salary for buying strawberries and ice. In order to make a perfect smoothie, he needs to put 10 strawberries and 5 cubes of ice per cup of smoothie. The price of a strawberry is $0.5 and the price of a cube of ice is $0.2. His weekly salary is $10."

b. Draw one of Monet’s indifference curves for strawberries and ice and explain the economic intuition. (I think I got this one)

c. How many strawberries and ice cubes will Monet buy? Show the answer either graphically or mathematically. (please help here)




I already found that the graph would intercept at 20 on the y axis and 50 on the x using the budget constraint equation. I just dont know how to figure out how much she should buy. someone help please.

These goods are perfect complements. We know they will always be used in the same proportion. Hence, we know we have "L" shaped indifference curves. Mathematically, we find the the the spot on the budget constraint where the utility is maximized by solving some equations

The proportions of consumption
10STrawberries = 5 Ice Or
2s=i

And the budget constraint
10=0.50S+0.20*i

Which equals
10= .5s+ .2*2s
10=.9s
S= 10/.9=11.11

Then
10=.5(11.11)+.2i
Gives
i=22.22